Geometry Quadrilaterals -1- NJCTL.org
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1 Name Date Lab: Quadrilaterals in the Coordinate Plane Objective In this lab you will investigate a specific quadrilateral. In your assigned groups you will look for special properties, such as parallel sides, congruent sides/diagonals, right angles and congruent diagonals. You will use algebraic tools such as the distance formula and slope formula to find these special properties. After analyzing the properties of your figure you will then classify your quadrilateral and explain. Your group will be graded on: Your ability to work with each other and communicate through your individual roles. The neatness and organization of your work. The completeness and accuracy of your answers. Your understanding and explanations of quadrilateral classification. Please see attached for Rubric. Roles: Time Keeper You have 30 minutes to complete this activity. Keep your group members informed of the time left, otherwise you will lose points. Recorder You are responsible for neatly writing the group member names on the blank paper provided. Also, you are to record all final calculations for the activity. Manager You are to ensure that all team members stay on task and contribute to the group. You are responsible for the completion of the activity. Checker You are to double-check all calculations for accuracy. You should also make sure that your group completes all necessary parts of the activity. Geometry Quadrilaterals -1- NJCTL.org
2 Grading Rubric Geometry Quadrilaterals -2- NJCTL.org
3 Quadrilaterals in the Coordinate Plane (A) Group: Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-2,2) O(1,6) H(6,6) S(3,2) Geometry Quadrilaterals -3- NJCTL.org
4 Part 2: Sides W(-2,2) O(1,6) H(6,6) S(3,2) Slope Length Diagonals Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Geometry Quadrilaterals -4- NJCTL.org
5 Quadrilaterals in the Coordinate Plane (B) Group: Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(1,-4) B(3,-1) L(7,-1) S(5,-4) Geometry Quadrilaterals -5- NJCTL.org
6 Part 2: W(1,-4) B(3,-1) L(7,-1) S(5,-4) Sides Slope Length Diagonals Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Geometry Quadrilaterals -6- NJCTL.org
7 Quadrilaterals in the Coordinate Plane (C) Group: Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: D(1,3) Q(2,5) R(8,2) P(7,0) Geometry Quadrilaterals -7- NJCTL.org
8 Part 2: D(1,3) Q(2,5) R(8,2) P(7,0) Sides Slope Length Diagonals Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Geometry Quadrilaterals -8- NJCTL.org
9 Quadrilaterals in the Coordinate Plane (D) Group: Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: A(4,0) B(7,4) C(3,7) D(0,3) Geometry Quadrilaterals -9- NJCTL.org
10 Part 2: A(4,0) B(7,4) C(3,7) D(0,3) Sides Slope Length Diagonals Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Geometry Quadrilaterals -10- NJCTL.org
11 Quadrilaterals in the Coordinate Plane (E) Group: Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-3,-1) B(-2,2) G(3,2) O(2,-1) Geometry Quadrilaterals -11- NJCTL.org
12 Part 2: W(-3,-1) B(-2,2) G(3,2) O(2,-1) Sides Slope Length Diagonals Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Geometry Quadrilaterals -12- NJCTL.org
13 Quadrilaterals in the Coordinate Plane (F) Group: Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: K(7,1) I(7,5) N(0,5) D(0,1) Geometry Quadrilaterals -13- NJCTL.org
14 Part 2: K(7,1) I(7,5) N(0,5) D(0,1) Sides Slope Length Diagonals Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Geometry Quadrilaterals -14- NJCTL.org
15 Quadrilaterals in the Coordinate Plane (A) Group: ANSWER KEY Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-2,2) O(1,6) H(6,6) S(3,2) Geometry Quadrilaterals -15- NJCTL.org
16 Part 2: Sides WO W(-2,2) O(1,6) H(6,6) S(3,2) Slope Length OH HS 4. WS Diagonals OS = WH = Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Quadrilateral WOSH is a rhombus because both pairs of opposite sides are parallel, all of the sides have a length of 5, and the diagonals are perpendicular. Since WOSH is a rhombus, it is also considered to be a parallelogram. Geometry Quadrilaterals -16- NJCTL.org
17 Quadrilaterals in the Coordinate Plane (B) Group: ANSWER KEY Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(1,-4) B(3,-1) L(7,-1) S(5,-4) Geometry Quadrilaterals -17- NJCTL.org
18 Part 2: W(1,-4) B(3,-1) L(7,-1) S(5,-4) Sides WB Slope 3 2 Length BL 0 4 LS WS 0 4 Diagonals BS 3 2 WL = Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Quadrilateral WBLS is a parallelogram because both pairs of opposite sides are parallel and congruent. There are no perpendicular lines (so no right angles), and the sides are not all congruent. Therefore, parallelogram WBLS is not a rhombus, rectangle, or a square. Geometry Quadrilaterals -18- NJCTL.org
19 Quadrilaterals in the Coordinate Plane (C) Group: ANSWER KEY Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: D(1,3) Q(2,5) R(8,2) P(7,0) Geometry Quadrilaterals -19- NJCTL.org
20 Part 2: D(1,3) Q(2,5) R(8,2) P(7,0) Sides Slope Length DQ QR = RP DP 1 2 Diagonals DR = = QP 1 50 = Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Quadrilateral DQRP is a rectangle because both pairs of opposite sides are parallel and congruent. Also, the adjacent sides are perpendicular to each other, which form 4 right angles. Also, the diagonals are congruent. Therefore, quadrilateral DQRP is a rectangle. Since DQRP is a rectangle, it is also considered to be a parallelogram. Geometry Quadrilaterals -20- NJCTL.org
21 Quadrilaterals in the Coordinate Plane (D) Group: ANSWER KEY Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: A(4,0) B(7,4) C(3,7) D(0,3) Geometry Quadrilaterals -21- NJCTL.org
22 Part 2: A(4,0) B(7,4) C(3,7) D(0,3) Sides AB Slope 4 3 BC 3 4 CD 4 3 AD 3 4 Diagonals DB 1 7 Length = CA 7 50 = Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Quadrilateral ABCD is a square because it has the qualities of all of the quadrilaterals listed above. Both pairs of opposite sides are parallel, so it s considered to be a parallelogram. Adjacent sides are perpendicular and the diagonals are congruent, so it s considered to be a rectangle. All 4 sides are congruent, and the diagonals are perpendicular, so it is also considered a rhombus. Since it has the qualities of both a rhombus and a rectangle, quadrilateral ABCD is a square. Geometry Quadrilaterals -22- NJCTL.org
23 Quadrilaterals in the Coordinate Plane (E) Group: ANSWER KEY Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-3,-1) B(-2,2) G(3,2) O(2,-1) Geometry Quadrilaterals -23- NJCTL.org
24 Part 2: W(-3,-1) B(-2,2) G(3,2) O(2,-1) Sides Slope Length WB BG 0 5 GO WO 0 5 Diagonals BC 3 4 WG = Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Quadrilateral WBLS is a parallelogram because both pairs of opposite sides are parallel and congruent. There are no perpendicular lines (so no right angles), and the sides are not all congruent. Therefore, parallelogram WBLS is not a rhombus, rectangle, or a square. Geometry Quadrilaterals -24- NJCTL.org
25 Quadrilaterals in the Coordinate Plane (F) Group: ANSWER KEY Time Keeper: Recorder: Manager: Checker: Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: K(7,1) I(7,5) N(0,5) D(0,1) Geometry Quadrilaterals -25- NJCTL.org
26 Part 2: K(7,1) I(7,5) N(0,5) D(0,1) Sides Slope Length ND undefined 4 NI 0 7 IK undefined 4 KD 0 7 Diagonals NK 4 7 DI Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals. a. Parallelogram b. Rectangle c. Rhombus d. Square Quadrilateral NIKD is a rectangle because both pairs of opposite sides are parallel and congruent. Also, the adjacent sides are perpendicular to each other, which form 4 right angles. Also, the diagonals are congruent. Therefore, quadrilateral NIKD is a rectangle. Since NIKD is a rectangle, it is also considered to be a parallelogram. Geometry Quadrilaterals -26- NJCTL.org
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